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Time series forecasting requires capturing patterns across multiple temporal scales while maintaining computational efficiency. This paper introduces AWGformer, a novel architecture that integrates adaptive wavelet decomposition with…
Simulating the long-term dynamics of multi-scale and multi-physics systems poses a significant challenge in understanding complex phenomena across science and engineering. The complexity arises from the intricate interactions between scales…
The dynamics of Lagrangian particles in turbulence play a crucial role in mixing, transport, and dispersion in complex flows. Their trajectories exhibit highly non-trivial statistical behavior, motivating the development of surrogate models…
Many phenomena are described by bivariate signals or bidimensional vectors in applications ranging from radar to EEG, optics and oceanography. The time-frequency analysis of bivariate signals is usually carried out by analyzing two separate…
Dynamic link prediction plays a crucial role in diverse applications including social network analysis, communication forecasting, and financial modeling. While recent Transformer-based approaches have demonstrated promising results in…
Time series measured from real-world systems are generally noisy, complex and display statistical properties that evolve continuously over time. Here, we present a method that combines wavelet analysis and non-stationary surrogates to…
The treatment of Hall-effect thrusters as nonlinear, dynamical systems has emerged as a new perspective to understand and analyze data acquired from the thrusters. The acquisition of high-speed data that can resolve the characteristic…
A new and an enriched JPEG algorithm is provided for identifying redundancies in a sequence of irregular noisy data points which also accommodates a reference-free criterion function. Our main contribution is by formulating analytically…
The versatility of self-attention mechanism earned transformers great success in almost all data modalities, with limitations on the quadratic complexity and difficulty of training. To apply transformers across different data modalities,…
For numerous parameter and state estimation problems, assimilating new data as they become available can help produce accurate and fast inference of unknown quantities. While most existing algorithms for solving those kind of ill-posed…
We provide a nonparametric method for the computation of instantaneous multivariate volatility for continuous semi-martingales, which is based on Fourier analysis. The co-volatility is reconstructed as a stochastic function of time by…
The empirical wavelet transform is an adaptive multiresolution analysis tool based on the idea of building filters on a data-driven partition of the Fourier domain. However, existing 2D extensions are constrained by the shape of the…
The challenge of quantifying uncertainty propagation in real-world systems is rooted in the high-dimensionality of the stochastic input and the frequent lack of explicit knowledge of its probability distribution. Traditional approaches show…
The performance of machine learning surrogates is critically dependent on data quality and quantity. This presents a major challenge, as high-fidelity (HF) data is often scarce and computationally expensive to acquire, while low-fidelity…
Multivariate time series with long-dependence are observed in many applications such as finance , geophysics or neuroscience. Many packages provide estimation tools for univariate settings but few are addressing the problem of…
A wavelet-like model for distributions of objects in natural and man-made terrestrial environments is developed. The model is constructed in a self-similar fashion, with the sizes, amplitudes, and numbers of objects occurring at a constant…
Effective learning of asymmetric and local features in images and other data observed on multi-dimensional grids is a challenging objective critical for a wide range of image processing applications involving biomedical and natural images.…
Surrogate testing is used widely to determine the nature of the process generating the given empirical sample. In the present study, the usefulness of phase-randomized surrogates, amplitude adjusted Fourier transform (AAFT) and iterated…
There has been a recent surge of interest in time series modeling using the Transformer architecture. However, forecasting multivariate time series with Transformer presents a unique challenge as it requires modeling both temporal…
Estimating accurate high-dimensional transformations remains very challenging, especially in a clinical setting. In this paper, we introduce a multiscale parameterization of deformations to enhance registration and atlas estimation in the…